- #1

Pouyan

- 103

- 8

## Homework Statement

Calculate the force of magnetic attraction between the northern and southern hemispheres of a uniformly charged spinning spherical shell, with radius R, angular velocity ω and surface charge density σ.

## Homework Equations

Maxwell Tensor : T

_{m}= [/B](1/μ) *

**((B*n)B - (1/2)***B

^{2}

**n)**

B_in =(2/3)*μσRω

B_in =

***z**

B_out =μm

B_out =

**/(**4πr

^{3}

**) * (**2cosθ

**r +**sinθ

**θ)**

wherem = (4/3)*πR

where

^{3}(σωR)

## The Attempt at a Solution

I do see in my solution that :

1-We use a surface consisting of the entire

**equatorial plane**, CLOSING IT with a hemispherical surface at infinity where (since the field is zero out there) contribution is zero.

for r>R :

B = μm/(4πr

^{3})

**θ =**- μm/(4πr

^{3})

**z (Why ?! )**

2-We have a equatorial circular disk. We use B inside and da = rdrdφ. Direction is in z-axis!

2-

**I don't want the solution because I already have it but MY QUESTIONS are :**

A) How should think and imagine this spheres ?!

Should I think like this and use those formulas :

B) Why we do write B = μm/(4πr

I know the rest. That is just integrating

A) How should think and imagine this spheres ?!

Should I think like this and use those formulas :

B) Why we do write B = μm/(4πr

^{3})**θ =**- μm/(4πr^{3})**z**

Why is θ =-z in this case ?! I don't get it !Why is θ =-z in this case ?! I don't get it !

I know the rest. That is just integrating